Our Constitution does not mandate the traditional gendered definition of marriage, but neither does our Constitution condemn it. This Court, accordingly, should allow the public debate regarding marriage to continue through the democratic process, both in California and throughout the Nation.

We will have more shortly…

The proponents attempt to distinguish this case from Lawrence v. Texas:

No precedent or established constitutional precept justifies federal judicial intervention into this sensitive democratic process. This is not a case, like Lawrence v. Texas, 539 U.S. 558 (2003), where the State has punished as a crime “the most private human conduct, sexual behavior, and in the most private of places, the home,” or sought “to control a personal relationship that, whether or not entitled to formal recognition in the law, is within the liberty of persons to choose without being punished as criminals.” Id. at 567. By reaffirming the traditional definition of marriage, the People of California have not even discouraged, let alone criminalized, any private behavior or personal relationship.

Then they attempt to distinguish Brown v. Board of Education and Loving v. Virginia:

Finally, this is not a case like Loving v. Virginia, 388 U.S. 1 (1967), or Brown v. Board of Education, 347 U.S. 483 (1954), where the State had embraced explicit “racial discrimination” of the sort “it was the object of the Fourteenth Amendment to eliminate.” Loving, 388 U.S. at 11. By enforcing “the central meaning of the Equal Protection Clause” in those cases, id. at 12, this Court vindicated a constitutional norm that the People of this Nation had fought and died to establish and had expressly and democratically enacted as an Amendment to the Constitution. And while the antimiscegenation laws invalidated in Loving had existed in some (though by no means all) of the States for part of this Nation’s history, race was ever understood to play a fundamental part in the definition of marriage.

Here is a brief summary of proponents’ argument on Article III standing:

Petitioners have standing to defend Proposition 8 in lieu of public officials who have declined to do so. A State unquestionably has standing to defend the constitutionality of its laws, and this Court’s decisions establish that state law determines who is authorized to assert this interest on behalf of the State. Here, the California Supreme Court has squarely held that the proponents are authorized to assert this interest when public officials decline to defend an initiative

They appear to argue that restricting marriage to opposite-sex-couples-only prevents those opposite-sex couples from harming society by reproducing outside of marriage:

Throughout human history, societies have regulated sexual relationships between men and women so that the unique procreative capacity of such relationships benefits rather than harms society. In particular, an animating purpose of marriage is to increase the likelihood that children will be born and
raised in stable and enduring family units by their own mothers and fathers. Because relationships between persons of the same sex do not have the capacity to produce children, they do not implicate this interest in responsible procreation and childrearing in the same way. The Equal Protection Clause does not require the State to ignore this difference. See, e.g., Board of Trs. of the Univ. of Ala. v. Garrett, 531 U.S. 356, 366-67 (2001).

They argue that if the Court should find that proponents lack Article III standing, then both the appeals court and district court decisions should be vacated:

If this Court holds, contrary to the foregoing, that Petitioners lack standing to defend Proposition 8 on appeal, the Court would then “have an obligation. . . to inquire not only into this Court’s authority to decide the questions petitioners present, but to consider, also, the authority of the lower courts to proceed.” Id. at 73. Obviously, the Ninth Circuit’s judgment would have to be vacated. See FW/PBS, Inc. v. City of Dallas, 493 U.S. 215, 235-36 (1990). In addition, the sweeping opinion and state-wide injunction entered by the trial court should be vacated as well

And they argue that Prop 8 protects the First Amendment:

As our amici will demonstrate, Proposition 8 advances other important societal interests in addition to those we address, including accommodating the First Amendment and other fundamental rights of institutions and individuals who support the traditional definition of marriage on religious or moral grounds.